Optimal Boundary Control of a Thermal System: Inverse Conduction Problem

Abstract

The nonlinear inverse heat conduction problem is the calculation of surface heat fluxes and temperatures in materials possessing variable temperature properties. The model considered in this paper, is the nonlinear heat equation. The volumic specific heat and the conductivity are dependent of the temperature. An output least square method is used to solve the problem. It consists in minimizing a criterion J in order to natch the computed outputs of the model to the temperature measurements. The unknown heat flux is then calculated as a solution of an optimal boundary control problem. Minimizing J is performed with the classical conjugate gradient method. Gradient components are calculated by introducing a Lagrangian.The method works satisfatorily in simulation. Experimental results are reported. The data are the temperature measurements given by four sensors inside a plexiglas sample. In order to evaluate the feasibility of the method in a realistic situation, the experimental heat flux is also measured and compared with the computed flux.